Question

The sum of two numbers is 37. The smaller number is 9 less than the larger number. What are the numbers?

Larger number:
Smaller number:

Answer 1

Larger number = 23; Smaller number = 14.

Explanation:

Let's assign variables and numbers based on what we know from the world problem. *NOTE: It doesn't have to be x or y. It can be different letters like: s or t.*

Let x be smaller number = y- 9 ;

Let y be larger number.

Problem: x + y = 37.

STEP 1: Since x = y- 9...

(y-9) + y = 37

STEP 2: Open the brackets...

y - 9 + y = 37

STEP 3: COLLECT LIKE TERMS (CLT)...

2y - 9 = 37

STEP 4: Add 9 to both other sides...

2y = 46

STEP 5: Bring divide 2 from both sides.

y = 23.

STEP 6: Since y = 23 & x = y - 9

x = 23 - 9

STEP 7: COLLECT LIKE TERMS (CLT)...

x = 14.

Let's check:

x = y - 9

x = 23 - 9

x = 14. ✔

x + y = 37

23 + 14 = 37. ✔

Credentials: Grade 12 knowledge. Studying at Ontario, Canada, for Grade 12 College Math.